# Structures and Observables

## Axel Maas

## The concepts of quantum field theory

Most modern fundamental theories of nature are gauge theories. These are complex theories, in which the observable consequences are highly non-linearly connected to the elementary particles and interactions. Especially, the particles we measure are often emergent ones.

Using analytical methods and large-scale numerical simulations we uncover the structures leading to this emergence, and determine what we can see at experiments. As the underlying mechanisms are often similar, we do so for a wide range of theories, covering electroweak physics and the Higgs, dark matter, grand-unified theories to quantum gravity and beyond. Our work therefore covers the primary laws of nature, from which all physics descends. Our results range from conceptual answers like how a universe is described in quantum gravity, to very concrete experimental predictions like cross sections measurable at colliders like the LHC at CERN in Higgs physics.

Since such theories often contain redundancies and objects, which by themselves can only be auxiliaries, this poses important questions about the ontology of particle physics, i.e. the question, what is real. Aiming at understanding these questions connects our work to philosophy of physics.

### Specific Research topics

**What we do in detail**

Our primary research actiivity center around creating a bridge from a fundamental understanding of quantum gauge theories to their phenomenology. The particular aim is to identify and understand phenomena, which cannot be captured with standard perturbative means, and how they manifest the genuine non-linear structure of quantum theories. Our story so far can be read in two reviews articles, on Brout-Englert-Higgs physics: From foundations to phenomenology and Gauge bosons at zero and finite temperature.

**Foundations of quantum-gauge-field theories**

So-called gauge theories represent the most common version of particle physics theories. Especially the standard model, but also gravity, and most of their speculated extensions belong to this category. While they have been extremely successful in the description of nature, several very fundamental issues of them are still poorly understood.

One of them is what their physical degrees of freedom are, and how they emerge from the fundamental ones. This entails especially the question of how the mathematical structure is related to the physically observable one. The complex geometric structure of gauge theories made this a challenging problems since more than half a century.

Our aim is to explicitly construct physically observable particle spectra. Likewise, we determine how they are made up from the elementary degrees of freedom, and what kind of mathematical-geometrical structure governs their relation.

**Standard model physics**

The discovery of the Higgs boson has been one of the greatest scientific discoveries of the recent years. It is the last element of the standard model of particle physics, and a possible gateway to whatever lies beyond. With this discovery, the properties of the Higgs came into the focus of investigations.

The theory underlying the Higgs sector has plenty of enigmas so far. One is that it is not even clear, whether it a real theory, or whether new physics is mandatory to make it a real theory. The other is that there are subtle effects which are not yet accounted for, but which could provide distinct new signatures, like states containing several Higgs bosons or deviations from expectations in experiments.

To fully understand Higgs physics, we investigate and simulate numerically electroweak, Higgs, flavor and top physics in the standard model. We determine signatures for the LHC and future colliders. We furthermore use our understanding of gauge theories to infer how Brout-Englert-Higgs physics work.

**Unifying interactions**

The standard model has a very peculiar, regular structure. This suggests the existence of an underlying ordering principle, a unifying theory. We expect that such a unifying theory needs to involve the Brout-Englert-Higgs effect to create the apparent independent known interactions, the electromagnetic one, the weak one, and the strong one.

We therefore study how generalized Brout-Englert-Higgs effects act, and how they can help to shape both the known interactions and the flavor structure of the standard model. Especially important are here how the spectrum of known particles emerges in the process. This not only includes known particles, but also dark matter.

Finally, it is not clear how a quantum theory of gravity can factor into this picture. We therefore study how gravity and the Brout-Englert-Higgs effect interact, and also supersymmetry as a possible unifying concept of particle physics and quantum gravity.

### Teaching

Current lectures

- Beyond the Standard Models (WS 24/25)
- Methods of theoretical physics for future teachers (WS 24/25)
- Philosophy of Physics: Symmetries (WS 24/25)

Lecture notes

Topic | Level | Hours | Last updated |

Anomalies | PhD | 4 hours | July 2014 |

Advanced General Relativity and Quantum Gravity | Master, QFT recommended | 2 hours/week | March 2024 |

Advanced Mathematical Methods | Master | 3 hours/week | January 2024 |

Astroparticle Physics | Master, QFT recommended | 2 hours/week | June 2021 |

Beyond the Standard Model | Master, requires QFT | 3 hours/week | June 2018 |

Electroweak Physics | Master, requires QFT | 2 hours/week | February 2021 |

Group theory | Master | 2 hours/week | January 2016 |

Hadronphysics | Master, requires QFT | 2 hours/week | March 2023 |

Introduction to Mathematics | Bachelor | 1 hour/week | September 2023 |

Lattice quantum field theory | Master, requires QFT | 2 hours/week | June 2020 |

Linear algebra | Bachelor | 2 hours/week | September 2023 |

Modern chapters of theoretical physics | Bachelor | 2 hours/week | June 2021 |

Methods of Theoretical physics for teachers | Master | 3 hours/week | October 2022 |

Nuclear and particle physics | Master/Teacher of physics | 2 hours/week | June 2016 |

Philosophy of Physics | Bachelor/Master/PhD | 2 hours/week | July 2018 |

Programming in Mathematica and C(++) | Bachelor | 2 hours/week | June 2018 |

Quantum Field Theory I | Master | 3 hours/week | March 2023 |

Quantum Field Theory II | Master, requires QFT I (in parallel) | 4 hours/week | January 2020 |

Quantum mechanics | Bachelor | 4 hours/week | May 2022 |

Theoretical Mechanics | Bachelor | 4 hours/week | February 2017 |

Theoretical Particle Physics | Master | 2 hours/week | February 2014 |

Theoretical Particle Physics | Master | 4 hours/week | September 2015 |

Standard Model of particle physics | Master, requires QFT | 2 hours/week | July 2011 |

Supersymmetry | Master, requires QFT | 2 hours/week | October 2022 |

### Open and finished theses

### Publications

Review articles

- A. Maas, The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy (Springer Nature (Cham), 2305.01960 [hep-th]; May 2023)
- P. Berghofer et al., Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches (Cambridge Elements in Foundations of Contemporary Physics; 2110.00616 [physics.hist-ph]; October 2021)
- A. Maas, Brout-Englert-Higgs physics: From foundations to phenomenology (Prog. Part. Nucl. Phys. 106 (2019) 132; 1712.04721 [hep-ph]; December 2017)
- A. Maas, Gauge bosons at zero and finite temperature (Phys. Rep. 524 (2013) 203; 1106.3942 [hep-ph]; June 2011)
- A. Maas, Gluons at finite temperature in Landau gauge Yang-Mills theory (Mod. Phys. Lett. A, Vol. 20, No. 24 (2005) pp. 1797-1811; hep-ph/0506066; June 2005)

White papers

- J. Andersen et al., Les Houches 2023: Physics at TeV Colliders: Standard Model Working Group Report (2406.00708 [hep-ph], June 2024)

Foundations of quantum-gauge-field theories

- A. Maas, Constraining the gauge-fixed Lagrangian in minimal Landau gauge (SciPost Phys. 8, 071 (2020); arxiv:1907.10435 [hep-lat]; July 2019)
- A. Maas, Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge (Ann. of Phys. 387 (2017) 29; arxiv:1705.03812 [hep-lat]; May 2017)
- A. Maas, Gauge engineering and propagators (Quark Confinement and the Hadron Spectrum XII; arxiv:1610.05639 [hep-lat]; October 2016)
- A. Maas et al., Dyson-Schwinger equations and N=4 SYM in Landau gauge (Eur. Phys. J. C 76 113; arxiv:1512.06664 [hep-ph]; December 2015)
- A. Maas, More on the properties of the first Gribov region in Landau gauge (Phys. Rev. D 93 054504; arxiv:1510.08407 [hep-lat]; October 2015)
- A. Maas, Propagators and topology (Eur. Phys. J. C75 (2015) 122; arxiv:1410.7954 [hep-lat]; October 2014; Source code)
- A. Maas et al., Analytic and numerical study of the free energy in gauge theory (Phys. Rev. D 89, 034011 (2014); arxiv:1309.1957 [hep-lat]; September 2013)
- A. Maas et al., Bounds on free energy in QCD (Quark Confinement and the Hadron Spectrum X; arxiv: 1301.3520 [hep-lat]; January 2013)
- A. Maas, Local and global gauge-fixing (Quark Confinement and the Hadron Spectrum X; arxiv: 1301.2965 [hep-th]; January 2013)
- A. Maas, (Non-)Aligned gauges and global gauge symmetry breaking (Mod. Phys. Lett. A, Vol. 27, No. 38 (2012) 1250222; arxiv:1205.0890 [hep-th]; May 2012)
- A. Maas, On the structure of the residual gauge orbit (II International Workshop on QCD Green"s Functions, Confinement and Phenomenology; PoS(QCD-TNT-II)028; arxiv: 1111.5457 [hep-th]; November 2011)
- A. Maas, Gauges, propagators, and physics (Quark Confinement and the Hadron Spectrum IX; AIP Conf. Proc. 1343 p182-184 (2011);arxiv: 1011.5409 [hep-ph]; November 2011)
- A. Maas, Scalar-matter-gluon interaction (The many faces of QCD; arxiv: 1102.0901 [hep-lat]; February 2011)
- A. Maas, On gauge fixing (28th international symposium on lattice field theory; arxiv: 1010.5719 [hep-lat]; October 2010)
- A. Maas et al., Strong-coupling study of the Gribov ambiguity in lattice Landau gauge (Eur. Phys. J. C68, p183 (2010); arxiv:0912.4203 [hep-lat]; December 2009)
- A. Maas, Constructing non-perturbative gauges using correlation functions (Phys. Lett. B689, p107 (2010); arxiv:0907.5185 [hep-lat]; July 2009)
- A. Maas, Green's Functions and Topological Configurations (Quark Confinement and the Hadron Spectrum VIII; arxiv: 0811.2730 [hep-lat]; November 2008)
- A. Maas, More on Gribov copies and propagators in Landau-gauge Yang-Mills theory (Phys. Rev. D79, 014505,2009; arxiv:0808.3047 [hep-lat]; August 2008)
- A. Maas, Instantons, monopoles, vortices, and the Faddeev-Popov operator eigenspectrum (18th International IUPAP conference on few-body problems in physics; Nucl. Phys. A790 566c-569c (2007); hep-th/0610011; October 2006)
- A. Maas, On the Faddeev-Popov operator eigenspectrum in topological background fields (I Latin American Workshop on High Energy Phenomenology; Braz.J.Phys.37N2B:514-519,2007; hep-th/0603087; March 2006)
- A. Maas, On the spectrum of the Faddeev-Popov operator in topological background fields (Eur.Phys.J. C48, No.1, 179-192; hep-th/0511307; November 2005)
- A. Fuster et al., BRST Quantization: a short review (Int. J. Geo. Meth. Mod. Phys., Vol. 2, No. 5 (2005) 939-963; 10th Saalburg Summer school on modern theoretical methods; hep-th/0506098; June 2005)

QCD and the QCD phase diagram

- A. Maas et al., More on the three-gluon vertex in SU(2) Yang-Mills theory in three and four dimensions (SciPost Phys. Core 5, 019 (2022), arXiv:2006.08248 [hep-lat], June 2020)
- O. Hajizadeh et al., Exploring the Tan contact term in Yang-Mills theory (Phys. Rev. D 103, 034023 (2021), arXiv:1909.12727 [hep-ph], September 2019)
- T. Boz et al., Finite-density gauge correlation functions in QC2D (Phys. Rev. D 99, 074514 (2019), arXiv:1812.08517 [hep-lat]; December 2018)
- R. Alkofer et al., Bound state properties from the Functional Renormalisation Group (Phys. Rev. D 99, 054029 (2019); arXiv: 1810.07955 [hep-ph]; October 2018)
- W. Mian et al., Formulating electroweak pion decays in functional methods (17th international conference on hadron physics; December 2017)
- O. Hajizadeh et al., Gluon and ghost correlation functions of 2-color QCD at finite density (35th international symposium on lattice field theory; arxiv:1710.06013 [hep-lat]; October 2017)
- J. Paris-Lopez et al., Calculating hadron properties from dynamical hadronization in the Functional Renormalisation Group (Fairness meeting 2017; October 2017)
- O. Hajizadeh et al., Constructing a neutron star in G2-QCD (Eur.Phys.J. A53 (2017) 207); arxiv:1702.08724 [astro-ph.HE]; February 2017)
- A. Maas et al., Influence of broken flavor and C and P symmetry on the quark propagator (Eur.Phys.J. A53 (2017) 22; arxiv:1611.08130 [hep-ph]; November 2016)
- W. Mian et al., Quark Propagator with electroweak interactions in the Dyson-Schwinger approach (Quark Confinement and the Hadron Spectrum XII; arxiv:1610.02936 [hep-ph]; October 2016)
- O. Hajizadeh et al., A G2-QCD neutron star (34th international symposium on lattice field theory; arxiv:1609.06979 [astro-ph.HE]; September 2016)
- L. Fister et al., Exploratory study of the temperature dependence of magnetic vertices in SU(2) Landau gauge Yang-Mills theory (Phys. Rev. D 90, 056008; arxiv:1406.0638 [hep-lat]; June 2014; Source code)
- A. Maas, Some more details of minimal-Landau-gauge Yang-Mills propagators (Phys. Rev. D 91, 034502 (2015); arxiv:1402.5050 [hep-lat]; February 2014)
- B. Wellegehausen et al., Hadron masses and baryonic scales in G2-QCD at finite density (Phys.Rev. D89 (2014) 056007; arxiv:1312.5579 [hep-lat]); December 2013)
- T. Mufti et al., Correlation Functions and Confinement in Scalar QCD (Combined proceeding for the conferences EPSHEP 2013, XXXI International Symposium on Lattice Field Theory, and QCD TNT3; 1310.8166 [hep-lat]; October 2013)
- L. von Smekal et al., G2-QCD: Spectroscopy and the phase diagram at zero temperature and finite density (31st international symposium on lattice field theory; 1310.7745 [hep-lat]; October 2013)
- E.-M. Ilgenfritz et al., Topological aspects of G2 Yang-Mills theory (Phys. Rev. D 86, 114508 (2012); arxiv:1210.5963 [hep-lat]; October 2012)
- A. Maas et al., G2 gauge theories (30th international symposium on lattice field theory; PoS(Lattice 2012)080; arxiv: 1210.7950 [hep-lat]; October 2012)
- M. Huber et al., Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results (JHEP 11 (2012) 035; arxiv:1207.0222 [hep-th]; July 2012)
- A. Maas et al., The phase diagram of a gauge theory with fermionic baryons (Phys. Rev. D 86, 111901(R) (2012); arxiv:1203.5653 [hep-lat]; March 2012)
- M. Dirnberger et al., No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory (Phys. Lett. B 716, 465 (2012); arxiv:1201.1360 [hep-lat]; January 2012)
- R. Alkofer et al., On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields (Quark Confinement and the Hadron Spectrum IX; AIP Conf. Proc. 1343 p179-181 (2011); arxiv: 1011.5831 [hep-ph]; November 2011)
- A. Maas et al., The gluon propagator close to criticality (Phys. Rev. D 95, 034037 (2012); arxiv: 1110.6340 [hep-lat]; October 2011)
- A. Maas et al., Yang-Mills Theory in lambda-Gauges (Phys. Rev. D 84, 114501 (2011); arxiv: 1108.2621 [hep-lat]; August 2011)
- A. Maas, On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators (JHEP 02 (2011) 076; arxiv: 1012.4284 [hep-lat]; December 2010)
- M. Blank et al., Aspects of gauge-(in)dependence in Bethe-Salpeter-equation studies of mesons (Phys. Rev. D 83, 034020 (2011); arxiv: 1007.3901 [hep-ph]; July 2010)
- C. S. Fischer et al., Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3) (Eur. Phys. J. C68, p165 (2010); arxiv: 1003.1960 [hep-lat]; March 2010)
- A. Maas, Describing gluons at zero and finite temperature (International Conference on Quarks and Nuclear Physics V; Chinese Journal of Physics 34, p1328 (2010); arxiv: 0911.0348 [hep-lat]; November 2009)
- E. Bilgici et al., Fermionic boundary conditions and the finite temperature transition of QCD (Few Body Systems 47 (2010) p125-135; arxiv:0906.3957 [hep-lat]; June 2009)
- R. Alkofer et al., Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory (Few Body Systems 47 (2010) p73-90; arxiv:0905.4594 [hep-ph]; May 2009)
- C. S. Fischer et al., Aspects of confinement from QCD correlation functions (Quark Confinement and the Hadron Spectrum VIII; arxiv: 0812.2745 [hep-ph]; December 2008)
- J. Danzer et al., Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory (JHEP 01 (2009) 024; arxiv:0810.3973 [hep-lat]; October 2008)
- C. S. Fischer et al., On the infrared behavior of Landau gauge Yang-Mills theory (Annals of Physics 324 (2009), pp. 2408-2437; arxiv:0810.1987 [hep-ph]; October 2008)
- T. Mendes et al., Infrared Propagators in MAG and Feynman gauge on the lattice (XIII International Conference on Selected Problems of Modern Theoretical Physics; arxiv: 0809.3741 [hep-lat]; September 2008)
- A. Cucchieri et al., Linear covariant gauges on the lattice (Comput.Phys.Commun.180:215-225,2009; arxiv:0806.3124 [hep-lat]; June 2008)
- A. Cucchieri et al., Three-point vertices in Landau-gauge Yang-Mills theory (Phys. Rev. D 77, 094510 (2008); arxiv:0803.1798 [hep-lat]; March 2008)
- A. Maas et al., A first look at Landau-gauge propagators in G2 Yang-Mills theory (JHEP 02 (2008) 070; arxiv:0711.1451 [hep-lat]; November 2007)
- C. S. Fischer et al., Large volume behavior of Yang-Mills propagators (XXV International Smyposium on Lattice Field theory; arxiv: 0709.3205 [hep-lat]; September 2007)
- A. Maas, Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory (Phys. Rev. D 75, 116004 (2007); arxiv:0704.0722 [hep-lat]; April 2007)
- A. Cucchieri et al., Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature (Phys. Rev. D 75, 076003 (2007); hep-lat/0702022; February 2007)
- A. Cucchieri et al., Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge (Mod.Phys.Lett.A22:2429-2438,2007; hep-lat/0701011; January 2007)
- C. S. Fischer et al., Large volume behaviour of Yang-Mills propagators (Annals Phys.322:2916-2944,2007; hep-ph/0701050; January 2007)
- A. Maas et al., Propagators in Yang-Mills theory for different gauges (Quark Confinement and the Hadron Spectrum VII; hep-lat/0610123; October 2006)
- A. Maas et al., On the infrared behavior of Green's functions in Yang-Mills theory (Infrared QCD in Rio; Braz. J. Phys. 37 No. 1B (2007), 219; hep-lat/0610006; October 2006)
- A. Cucchieri et al., Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory (Phys. Rev. D 74, 014503 (2006); hep-lat/0605011; May 2006)
- A. Maas, Solving a Set of Truncated Dyson-Schwinger equations with a globally converging methods (Comput. Phys. Commun., 175, 167-179 (2006); hep-ph/0504110; April 2005)
- A. Maas et al., The High-Temperature Phase of Landau-Gauge Yang-Mills theory (Eur.Phys.J. C42, No.1, 93-107 (2005); hep-ph/0504019; April 2005)
- W. Schleifenbaum et al., Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory (Phys. Rev. D72, 014017 (2005); hep-ph/0411052; November 2004)
- A. Maas et al., Finite-Temperature Yang-Mills Theory in Landau Gauge (Quark Confinement and the Hadron Sepctrum VI; AIP Conf. Proc. 756 (2005) 425; hep-ph/0411289; November 2004)
- W. Schleifenbaum et al., The Ghost-Gluon Vertex in Landau Gauge Yang-Mills Theory (42nd International School on Subnuclear Physics; hep-ph/0411060; November 2004)
- B. Grüter et al., Temperature Dependence of Gluon and Ghost Propagators in Landau-Gauge Yang-Mills Theory below the Phase Transition (Eur.Phys.J. C42, No. 1, 109-118 (2005); hep-ph/0408282; August 2004)
- A. Maas et al., High-Temperature Limit of Landau-Gauge Yang-Mills Theory (Eur.Phys.J. C37, No.3, 335-357 (2004); hep-ph/0408074; August 2004)
- A. Maas et al., Residual Confinement in High-Temperature Yang-Mills Theory (Strong and Electroweak Matter 2004; World Scientific, ISBN 981-256-135-8, April 2005; hep-ph/0408299; August 2004)
- B. Grüter et al., QCD Propagators at non-vanishing temperatures (25th International School on Nuclear Physics; Prog.Part.Nucl.Phys. 53 (2004) 343-345; hep-ph/0401164; January 2004)
- A. Maas et al., Towards the Finite Temperature Gluon Propagator in Landau Gauge Yang-Mills Theory (40th International School on Subnuclear Physics: From Quarks and Gluons to Quantum Gravity, Subnuclear Series No. 40, World Scientific, ISBN 981-238-613-0, Dec. 2003; hep-ph/0210178; October 2002)

Higgs and electroweak physics

- A. Maas, Experimental signatures of subtleties in the Brout-Englert-Higgs mechanism (57th Rencontres de Moriond, arxiv: 2305.07395 [hep-ph]; May 2023)
- A. Maas et al., Restoring the Bloch-Nordsieck theorem in the electroweak sector of the standard model (Phys. Rev. D 108, 013001 (2023); arxiv: 2212.08470 [hep-ph]; December 2022)
- B. Riederer et al., Investigating vector boson scattering: A fully gauge-invariant study (39th international symposium on lattice field theory, arxiv: 2210.17211 [hep-lat]; October 2022)
- P. Jenny et al., Vector boson scattering from the lattice (Phys. Rev. D 105, 114513 (2022); arxiv: 2204.02756 [hep-lat]; April 2022)
- F. Reiner et al., Bloch-Nordsieck restoration in llbar -> qqbar (EPS Conference on High Energy Physics 2021; arxiv: 2110.07312 [hep-ph]; October 2021)
- V. Afferrante et al., Testing the mechanism of lepton compositness (SciPost Phys. 10, 062 (2021); arxiv:2011.02301 [hep-lat]; November 2020)
- A. Maas et al., Gauge-invariant description of the Higgs resonance and its phenomenological implications (Phys. Rev. D 102, 113001 (2020); arxiv:2009.06671 [hep-ph]; September 2020)
- S. Fernbach et al., Constraining the Higgs valence contribution in the proton (Phys. Rev. D 101, 114018 (2020) ; arxiv:2002.01688 [hep-ph]; February 2020)
- A. Maas et al., Probing standard-model Higgs substructures using tops and weak gauge bosons (EPS Conference on High Energy Physics 2019; arxiv:1910.14316 [hep-ph]; October 2019)
- A. Maas et al., Exploratory study of the off-shell properties of the weak vector bosons (Phys. Rev. D 99, 074509 (2019); arxiv:1811.03395 [hep-lat]; November 2018)
- A. Maas et al., Implications of strict gauge invariance for particle spectra and precision observables (EPS Conference on High Energy Physics 2017; arxiv:1710.01182 [hep-ph]; October 2017)
- L. Egger et al., Pair production processes and flavor in gauge-invariant perturbation theory (Mod. Phys. Lett. A 32, 1750212 (2017); arxiv:1701.02881 [hep-ph]; January 2017)
- A. Maas, The quenched SU(2) fundamental scalar propagator in minimal Landau gauge (Eur. Phys. J. C76 (2016) 366; arxiv:1603.07525 [hep-lat]; March 2016; Code)
- A. Maas et al., A spectroscopical analysis of the phase diagram of Yang-Mills-Higgs theory (Phys. Rev. D 91, 113011; arxiv:1412.6440 [hep-lat]; December 2014)
- A. Maas et al., On the phase diagram and the singlet scalar channel in Yang-Mills-Higgs theory (32nd international symposium on lattice field theory; arxiv:1410.7935 [hep-lat]; October 2014)
- A. Maas et al., Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory (JHEP 1404 (2014) 006; arxiv:1312.4873 [hep-lat]; December 2013)
- A. Maas et al., Exploring Higgs Sector Spectroscopy (31st international symposium on lattice field theory; 1310.7832 [hep-lat]; October 2013)
- A. Maas et al., Non-perturbative aspects in a weakly interacting Higgs sector (36th International Conference on High-Energy Physics; arxiv: 1211.5301 [hep-lat]; November 2012)
- A. Maas, Bound-state/elementary-particle duality in the Higgs sector and the case for an excited 'Higgs' within the standard model (Mod. Phys. Lett. A, Vol. 28, No. 28 (2013) 1350103; arxiv:1205.6625 [hep-lat]; May 2012)
- A. Maas, Employing the perturbative definition of the Higgs mass in a non-perturbative calculation (29th international symposium on lattice field theory; arxiv: 1110.0908 [hep-lat]; October 2011)
- V. Macher et al., A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems (International Journal of Modern Physics A Vol. 27, No. 18 (2012) 1250098; arxiv: 1106.5381 [hep-ph]; June 2011)
- A. Maas, Accessing the properties of an elementary Higgs beyond perturbation theory (35th international conference on high-energy physics; November 2010)
- A. Maas, Accessing directly the properties of fundamental scalars in the confinement and Higgs phase (Eur. Phys. J. C71, p1548 (2011); arxiv: 1007.0729 [hep-lat]; July 2010)

Physics beyond the standard model

- Y. Dengler et al., Scattering of dark pions in Sp(4) gauge theory (arxiv: 2405.06506 [hep-lat], May 2024)
- Y. Dengler et al., Scattering of dark pions in an Sp(4) gauge theory (40th international symposium on lattice field theory, arXiv: 2311.18549 [hep-lat], December 2023)
- A. Maas et al., The manifestly gauge-invariant spectrum of the Minimal Supersymmetric Standard Model (arxiv: 2307.10282 [hep-ph], July 2023)
- E. Bennett et al., Singlets in gauge theories with fundamental matter (Phys. Rev. D 109, 034504 (2024), arxiv: 2304.07191 [hep-lat], April 2023)
- E. Dobson et al., The spectrum of GUT-like gauge-scalar models (39th international symposium on lattice field theory, arxiv: 2211.16937 [hep-lat], November 2022)
- F. Zieler et al., Strongly Interacting Dark Matter from
*S**p*(4) Gauge Theory, (Quark Confinement and the Hadron Sepctrum XV, arxiv: 2211.11272 [hep-ph], November 2022) - E. Dobson et al., Multiple breaking patterns in the Brout-Englert-Higgs effect beyond perturbation theory (Annals of Physics 457 (2023) 169404; arxiv: 2211.05812 [hep-lat], November 2022)
- F. Zierler et al., Singlet Mesons in Dark
*S**p*(4) Theories (39th international symposium on lattice field theory; 2210.11187 [hep-lat], October 2022) - S. Kulkarni et al., Low-energy effective description of dark Sp(4) theories (arxiv: 2202.05191 [hep-ph]; February 2022)
- E. Dobson et al., Exploring SU(3)-Higgs theories (38th international symposium on lattice field theory; arxiv:2110.15670 [hep-lat]; October 2021)
- A. Maas et al., Strong isospin breaking in Sp(4) gauge theory (38th international symposium on lattice field theory; arxiv:2109.14377 [hep-lat]; September 2021)
- V. Afferrante et al., A composite massless vector boson (Phys. Rev. D 101, 114506 (2020); arxiv:2002.08221 [hep-lat]; February 2020)
- V. Afferrante et al., Toward the spectrum of the SU(2) adjoint Higgs model (ALPS 2019; arxiv:1906.11193 [hep-lat]; June 2019)
- A. Maas, The quenched SU(2) scalar-gluon vertex in minimal Landau gauge (Phys. Rev. D 99, 114503 (2019), arxiv:1902.10568 [hep-lat]; February 2019; Code)
- A. Maas, The quenched SU(2) adjoint scalar propagator in minimal Landau gauge (Phys. Rev. D 99, 054504 (2019), arxiv:1809.08929 [hep-lat]; September 2018; Code)
- P. Törek et al., On observable particles in theories with a Brout-Englert-Higgs effect (ALPS 2018; arxiv:1806.11373 [hep-lat]; June 2018)
- A. Maas et al., The spectrum of an SU(3) gauge theory with a fundamental Higgs field (Annals of Physics 397, 303 (2018); arxiv:1804.04453 [hep-lat]; April 2018)
- P. Törek et al., A study of how the particle spectra of SU(N) gauge theories with a fundamental Higgs emerge (35th international symposium on lattice field theory; arxiv:1710.01941 [hep-lat]; October 2017)
- A. Maas et al., On the observable spectrum of theories with a Brout-Englert-Higgs effect (Annals of Physics 402 18 (2019); arxiv:1709.07477 [hep-ph]; September 2017)
- P. Törek et al., Testing gauge-invariant perturbation theory (34th international symposium on lattice field theory; arxiv:1610.04188 [hep-lat]; October 2016)
- A. Maas et al., Predicting the singlet vector channel in a partially Higgsed gauge theory (Phys. Rev. D 95, 014501; arxiv:1607.05860 [hep-lat]; July 2016)
- A. Maas et al., Gauge invariance and the physical spectrum in the two-Higgs-doublet model (Phys. Rev. D 93, 056005; arxiv:1601.02006 [hep-ph]; January 2016)
- P. Törek et al., Towards the spectrum of a GUT from gauge invariance (27th International Symposium on Lepton Photon Interactions at High Energies; arxiv:1509.06497 [hep-ph]; September 2015)
- A. Maas, Field theory as a tool to constrain new physics models (Mod. Phys. Lett. A, 30, 1550135 (2015); arxiv:1502.02421 [hep-ph]; February 2015)
- A. Maas, Observables in Higgsed Theories (37th International Conference on High-Energy Physics; arxiv:1410.2740 [hep-lat]; October 2014)
- D. August et al., The anomalous mass dimension from the techniquark propagator in Minimal Walking Technicolor (31st international symposium on lattice field theory; November 2013)
- D. August et al., On the Landau-gauge adjoint quark propagator (JHEP 01 (2013) 001; arxiv:1304.4423 [hep-lat]; April 2013)
- A. Maas, On the gauge boson's properties in a candidate technicolor theory (JHEP 05 (2011) 077; arxiv: 1102.5023 [hep-lat]; February 2011)
- E. Bilgici et al., Adjoint quarks and fermionic boundary conditions (JHEP 11 (2009) 035; arxiv:0904.3450 [hep-lat]; April 2009)

Quantum gravity

- A. Maas, Towards testing the Fröhlich-Morchio-Strocchi mechanism in quantum gravity (ICHEP 2022, arxiv: 2209.10961 [hep-th], September 2022)
- A. Maas et al., Exploratory applications of the Fröhlich-Morchio-Strocchi mechanism in quantum gravity (Phys.Rev.D 107, 025013 (2023); arxiv: 2202.05117 [hep-th]; Februrary 2022)
- A. Maas, The Fröhlich-Morchio-Strocchi mechanism and quantum gravity (SciPost Phys. 8, 051 (2020), arxiv:1908.02140 [hep-th]; August 2019)

### Talks and presentations

Presentations at conferences and universities during the last five years from my students and myself

Topic | Title | When | Where | Occasion |

BSM Physics | Dark matter scattering | August 2024 | Frankfurt, Germany | Strong and Electroweak Matter 2024 |

BSM Physics | Dark matter scattering | August 2024 | Liverpool, UK | Lattice 2024 |

BSM Physics | The observable spectrum for GUT-like theories | August 2024 | Liverpool, UK | Lattice 2024 |

Higgs Physics | Subleading Higgs effects in e+ e- -> fermion+antifermion | July 2024 | Prague, Czech Republic | ICHEP 2024 |

Field Theory | Observable spetrum in theories with a Brout-Englert-Higgs effect | July 2024 | Graz, Austria | From Gauge Symmetries to Gauge-Invariant Approaches |

Higgs Physics | Electroweak Sudakov Logarithms | July 2024 | Graz, Austria | Parton Showers and Resummation 2024 |

Higgs Physics | Gauge invariance and observables in particle physics | April 2024 | Edinburgh, UK | University Seminar |

Outreach | Schwerkraft | April 2024 | Graz, Austria | Alicja Kwade @ Sol LeWitt's Wall. Performed |

Higgs Physics | Gauge invariance and observables in particle physics | March 2024 | Milano, Italy | University Seminar |

BSM Physics | Scattering of symplectic SIMP dark matter with lattice field theory | March 2024 | Munich, Germany | Quarkonia meet Dark Matter |

Higgs Physics | Gauge invariance and observables in particle physics | February 2024 | Brookhaven, USA | BNL Seminar |

Field Theory | Gauge invariance and observables in particle physics | December 2023 | Zürich, Switzerland | ETH & University Seminar |

BSM Physics | Scattering in a dark sector described by Sp(4) gauge theory | July 2023 | Fermilab, USA | Lattice 2023 |

Higgs Physics | New precision effects from the Brout-Englert-Higgs mechanism | April 2023 | Protoroz, Slovenia | Particle Physics from Early Universe to Future Colliders |

Higgs Physics | Experimental signatures of subtelties in the Brout-Englert-Higgs mechanism | March 2023 | Thuile, Italy | Recontres de Moriond |

Quantum Gravity | Physical Observables in Canonical Quantum Gravity | March 2023 | Nijmegen, Netherlands | University Seminar |

Quantum Gravity | Physical Observables in Canonical Quantum Gravity | February 2023 | Waterloo, Canada | Perimeter Institute Seminar |

Higgs Physics | New effects in precision Brout-Englert-Higgs physics | December 2022 | Ljubljana, Slovenia | JSI Seminar |

Outreach | "Dunkle Energie" und was Physiker damit meinen | November 2022 | Vienna, Austria | VHS Vienna |

Higgs Physics | Subleading effects for future lepton colliders | September 2022 | Leoben, Austria | ÖPG Meeting |

BSM Physics | A manifestly gauge-invariant treatment of the Minimal Supersymmetric Standard Model | September 2022 | Leoben, Austria | ÖPG Meeting |

Higgs Physics | Investigating vector boson scattering | August 2022 | Bonn, Germany | Lattice 2022 |

BSM Physics | Dark Isosinglet Mesons in Sp(4) Gauge Theory with Nf=2 | August 2022 | Bonn, Germany | Lattice 2022 |

BSM Physics | Strongly Interacting Dark Matter from Sp(4) Gauge Theory | August 2022 | Stavanger, Norway | Confinement and the Hadron Spectrum 2022 |

Quantum Gravity | A new approach to Observables in Quantum Gravity | July 2022 | Bologna, Italy | ICHEP 2022 |

Higgs Physics | Vector boson scattering from augmented perturbation theory | July 2022 | Bologna, Italy | ICHEP 2022 |

BSM Physics | Possible discrepancies in GUT spectra | July 2022 | Bologna, Italy | ICHEP 2022 |

BSM Physics | Composite Massless Vector Bosons | July 2022 | DESY Zeuthen, Germany | Institute Seminar |

BSM Physics | Sp(4) gauge theory on the Lattice | September 2021 | Innsbruck, Austria | ÖPG Meeting |

Higgs Physics | Measuring the size of the Higgs | April 2022 | Vienna, Austria | HEPHY Seminar |

Higgs Physics | Bloch-Nordsieck restoration for llbar->ttbar | July 2021 | Hamburg, Germany | EPSHEP 2021 |

BSM Physics | Isospin breaking for dark matter | July 2021 | Boston, USA | Lattice 2021 |

BSM Physics | SU(3)+Higgs theory: The adjoint case | July 2021 | Boston, USA | Lattice 2021 |

BSM Physics | The spectrum of grand-unified theories | July 2021 | Boston, USA | Lattice 2021 |

BSM Physics | Sp(4) SIMP Dark Matter on the lattice | June 2021 | Online, USA | LHCP 2021 |

Higgs Physics | Gauge invariant spectra of SU(2) theories with BEH effect | May 2021 | MIT. USA | Lattice colloquium |

BSM Physics | The spectrum of grand-unified theories | April 2021 | Online, Hungary | ACHT 2021 |

Outreach | Wie das Higgs unser Bild von Elementarteilchen verändert | March 2021 | Graz, Austria | Facetten der Physik |

Field Theory | Gauge fixing and the ghost DSE | March 2021 | Valencia, Spain | FunQCD |

Higgs Physics | Probing Standard-Model Higgs Substructures using Tops and Weak Gauge Bosons | March 2021 | Dortmund, Germany | DPG Spring Meeting |

Outreach | Wie das Higgs unser Bild von Elementarteilchen verändert | January 2021 | Vienna, Austria | VHS Vienna |

Higgs Physics | Gauge invariant spectra and FMS mechanism for gauge theories with BEH effect | October 2020 | Jena, Gemany | University Seminar |

Higgs Physics | Fermionic spectrum with fermion-Higgs bound states in a SU(2) Wilson-Yukawa model | August 2020 | Online, Asia | Asia-Pacific Symposium for Lattice Field Theory |

Quantum Gravity | Approaching a diffemorphism-invariant description of black hole and particle dynamics | April 2020 | Online, Canada | Miniworkshop on Quantum Gravity |

Quantum Gravity | The Fröhlich-Morcchio-Strocchi mechanism and quantum gravity | November 2019 | Online | Asymptotic Safety Seminar |

### Organized conferences

From gauge symmetries to gauge-invariant approaches

15th of July - 17th of July 2024

University of Graz, Austria

Parton Showers and Resummation 2024

2nd of July - 5th of July 2024

University of Graz, Austria

Bound states in QCD and beyond IV

15th of February - 18th of February 2022 (was cancelled because of COVID 19)

Schlosshotel Rheinfels, St. Goar, Germany

5th of November 2020 - 6th of November 2020

University of Graz, Graz, Austria

ALPS 2020: An Alpine LHC Physics Summit

13th of April 2020 - 18th of April 2020 (was cancelled because of COVID 19)

University Center Obergurgl, Obergurgl, Austria

ALPS 2019: An Alpine LHC Physics Summit

22nd of April 2019 - 27th of April 2019

University Center Obergurgl, Obergurgl, Austria

Bound states in QCD and beyond III

9th of April 2019 - 12th of April 2019

Schlosshotel Rheinfels, St. Goar, Germany

ALPS 2018: An Alpine LHC Physics Summit

15th of April 2018 - 20th of April 2018

University Center Obergurgl, Obergurgl, Austria

Bound states in strongly coupled systems

12th of March 2018 -16th of March 2018

Galileo Galieli Institute, Firenze, Italy

Bound states in QCD and beyond II

20th of February 2017 - 23rd of February 2017

Schlosshotel Rheinfels, St. Goar, Germany

Bound states and resonances (55th International University Week for Theoretical Physics)

13th of February - 17th of February 2017

Castle Röthelstein, Admont, Austria

Bound states in QCD and beyond

24th of March 2015 - 27th of March 2015

Schlosshotel Rheinfels, St. Goar, Germany

Strongly-interacting Field Theories III

16th of November 2013 - 16th of November 2013

University of Jena, Jena, Germany

Quarks, Gluons, and Hadronic Matter under Extreme Conditions II

18th of March 2013 - 21st of March 2013

Schlosshotel Rheinfels, St. Goar, Germany

Strongly-interacting Field Theories II

29th of November 2012 - 1st of December 2012

University of Jena, Jena, Germany

Quarks, Gluons, and Hadronic Matter under Extreme Conditions

15th of March 2011 - 18th of March 2011

Schlosshotel Rheinfels, St. Goar, Germany

Quarks, Hadrons, and the Phase Diagram of QCD

31st of August 2009 - 3rd of September 2009

Schlosshotel Rheinfels, St. Goar, Germany

Quarks and Hadrons in Strong QCD

17th of March 2008 - 20th of March 2008

Schlosshotel Rheinfels, St. Goar, Germany

## Group leader

Axel Maas

Foundations of gauge theories - Higgs and electroweak physics - QCD - New Physics and dark matter - Quantum Gravity

eMail: axel.maas(at)uni-graz.at or phone +43-316-380-5231 or Mastodon or BlueSky

## Master student

Max Pfandner

Higgs and electroweak physics

## Staff

Simon Plätzer

Dark Matter - Higgs physics and electroweak physics - New physics - Collider physics

eMail: simon.plaetzer(at)uni-graz.at

Complete list of publications from Inspire

## Bachelor student

Viktoria Keusch

Foundations of quantum-gauge field theories

eMail: vkeusch(at)student.tugraz.at